Correct.  Keep up the good work!

"...through whom we have received grace and apostleship to bring about the obedience of faith among all the Gentiles, for His name's sake..." Romans 1:1-5 (NAS)

"...has been made known to all the nations, leading to obedience of faith; ²⁷ to the only wise God, through Jesus Christ, be the glory forever. Amen." Romans 16:26-27 (NAS)

Faith that Leads to Obedience to the Gospel:

In Paul's letter to the Christians at Rome, he commends them for having obeyed from the heart the form of teaching to which they were committed:

But thanks be to God that though you were slaves of sin, you became obedient from the heart to that form of teaching to which you were committed, ¹⁸ and having been freed from sin, you became slaves of righteousness." Romans 6:17-18 (NAS)

In that same chapter (Romans 6), Paul reminds them of how their obedience to the gospel had freed them from sin:

"Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? ⁴ Therefore we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. ⁵ For if we have become united with Him in the likeness of His death, certainly we shall be also in the likeness of His resurrection, ⁶ knowing this, that our old self was crucified with Him, that our body of sin might be done away with, that we should no longer be slaves to sin; ⁷ for he who has died is freed from sin."   Romans 6:3-7 (NAS) 

For more information, see Lesson 1.

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